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On the Differential Invariants of the Laguerre Group

Published online by Cambridge University Press:  24 October 2008

Tadahiko Kubota
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Extract

1. In a paper “Beiträge zur Inversionsgeometric,” which will appear in the forthcoming volume of the Science Reports of the Tôhoku Imperial University, I have treated the problem of determining the necessary and sufficient condition in order that two plane curves which are given by natural equations should be transformable into each other by inversion. In connection with that paper I propose here to treat the analogous problem for Laguerre transformations:

Having given two plane curves, by natural equations, in which the functional relations are all supposed to be analytic, it is required to determine the necessary and sufficient condition in order that the two plane curves should be transformable into each other by a Laguerre transformation.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 22 , Issue 2 , May 1924 , pp. 113 - 123
Copyright
Copyright © Cambridge Philosophical Society 1924

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References

* Blaschke, W., ‘Unterauchungen über die Geometrie der Speere in der Euklidischen Ebene,’ Monalshefte für Math. u. Phys. 21, 1910.Google Scholar

† Scheffers, G., Einführung in die Theorie der Curven in der Ebene und im Raume, 1901, S. 208.Google Scholar

* Lie-Scheffers, , Vorlesungen über continuierliche Gruppen, S. 694Google Scholar, Study, E., ‘Zur Differentialgeometrie der analytischen Curven,’ Transactions of the American Mathematical Society, 10, 1909.CrossRefGoogle Scholar

* Liebmann, H., ‘Beiträge zur Inversionsgeometrie der Kurven,’ Sitzungsberichte der Münchener Akademie, 1923.Google Scholar